The length of the rectangle is 5 cm more than its width. The perimeter is 82 cm.

for two variables you need two equations but first, what you know

P = 82 cm

now the two eq. s

P = 2a + 2b

82 = 2a + 2b (you plugged in what you know)

a = b + 5

and now you put one in the other

82 = 2 (b + 5) + 2b

82 = 2b + 10 + 2b

82 - 10 = 4b

4b = 72 / : 4

b = 18

and now plug in b in the equation for a

a = b + 5

a = 18 + 5

a = 23

now check your work

P = 2a + 2b

82 = 2*23 + 2*18

82 = 46 + 36

82 = 82

The width is 18 because if you take 82 and subtract 10 for the 2 lengths (because we are using perimeter) you come out with 72. 72 divided by 4 is 18, the lengths are five more because we took away that 5 in the beginning.

W=18cm

L=23cm